FIG. 1 describes a non-limitative example of a hybrid transmission derived from this design principle. Said transmission, which is illustrated by publication WO2012/131259, includes a solid primary shaft 1 connected directly by means of a filtration system (shock-absorbing hub, “damper”, a dual mass flywheel or some other means) 2, to the flywheel 3 of a heat engine (not illustrated here). The solid shaft 1 carries an idler gear 4 capable of being connected to the latter by a first coupling system 5 (dog clutch, synchronizer, or some other type of coupling, progressive or otherwise). A hollow primary shaft 6 is connected to the rotor of an electric machine 7. The hollow shaft 6 carries two fixed gears 8, 9. It may be connected to the solid primary shaft 1 by means of the first coupling system 5. A secondary shaft 10 carries two idler gears 11 and 12. The idler gears 11 and 12 may be connected to the primary shaft by means of a second coupling system 13 (dog clutch, synchronizer, or some other type of coupling, progressive or otherwise). The secondary shaft 10 likewise carries a fixed gear 14 and a step-down gear 15, leading to a differential 16 connected to the wheels of the vehicle.
As indicated above, the first coupling means 5 may occupy at least three positions, in which:                the heat engine is decoupled from the drive train connecting the electric machine 7 to the wheels (sliding gear in the center), the transmission being in neutral mode or electric mode,        the heat engine drives the wheels with or without the assistance of the electric machine (sliding gear on the left), the transmission being in heat mode or hybrid mode, and        the heat engine and the electric machine 7 are coupled in such a way (sliding gear on the right) as to add their respective torques together, in the direction of the wheels, the transmission being in hybrid mode, or in a “roadside recharging” mode, in which the heat engine does not drive the wheels, but causes the electric machine to rotate as a generator in order to recharge the batteries of the vehicle.        
When a gearbox does not include means of mechanical synchronization between the idler gears and a secondary gearbox shaft, on which they require to be engaged and disengaged, the synchronization necessary for engagement and disengagement may be assured by controlling the speed of the primary shaft in order to “synchronize” it with the secondary shaft, close to the gear ratio. This control is performed by adjusting the torque supplied by the one or more drive sources driving the primary line of the gearbox. In the case of a hybrid transmission, such as that described below, these drive sources are the heat engine, the electric machine, or both of these, in a hybrid operating mode in which the two concentric primary shafts are rotationally associated (sliding gear on the right).
When the vehicle is in motion, the secondary shaft rotates in all the operating modes of the transmission (heat engine, hybrid, electric). The idler gear to be engaged on the new ratio rotates at a different speed from the secondary shaft. Synchronization of the idler gear on its shaft is essential. When the vehicle is stationary, the secondary gears may also be at rest. In this case, the sliding gear may be displaced in order to engage the idler gear without synchronization.
However, the vehicle may also be brought to a stop without the need for the secondary gears to be stationary. This is particularly true in the roadside charging mode for this transmission, where, if the vehicle moves off after the request to change gear. The teeth of the sliding gear then run the risk of coming into contact with that of the idler gear. When the vehicle is stationary, this crashing of the gears will be an unpleasant experience for the driver.